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Poincare Return Map

  1. Nov 1, 2009 #1
    How do I write u''+u*e^x = 0 as a planar system?
    Last edited: Nov 1, 2009
  2. jcsd
  3. Nov 2, 2009 #2
    Okay its:

    Let z=u', then z'=u''=-exp(x)*u.

    So the planar system is {u'=z,z'=-exp(x)*u}, or in matrix form, U'=A*U, where U is the column vector (u,z) and A is the 2x2 matrix (0,1,-exp(x),0).

    What can be said about the Poincare return map on the transversal u>0?
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